A 3D shape descriptor, which is usually an n dimensional vector defining the features of an entire 3D model or some part of the 3D model, is one of the basic tools in computer graphics technology. The 3D shape descriptor is widely used in many 3D model processing tasks, such as searching, symmetry discovery and modeling.
MITRA, N. J., GUIBAS, L. J., and PAULY, M. 2006, “Partial and approximate symmetry detection for 3D geometry”, ACM Trans. Gr. 25, 3, 560.568 proposes to uses the ratio of the curvature tensors at the sample points as the shape descriptor of sample points.
To improve the discriminative performance, a number of shape descriptors have been proposed. The following documents discussed some examples of known 3D shape descriptors:    (1) 3D shape contexts, M. Kortgen, G.-J. Park, M. Novotni, and R. Klein, “3D Shape Matching with 3D Shape Contexts”, the 7th Central European Seminar on Computer Graphics, 2003.    (2) Spin images, A. E. Johnson and M. Herbert, “Using Spin Images for Efficient Object Recognition in Cluttered 3D Scenes”, IEEE Trans. on PAMI, 21(5), pp. 433-449, 1999.    (3) Shape distributions, R. Osada, T. Funkhouser, B. Chazelle, and D. Dobkin, “Shape Distributions”, ACM Trans. on Graphics, 21(4), pp. 807-832, 2002.
The shape context described in the above document (1) applies a natural extension of 2D shape context proposed in S. Belongie, J. Malik and J. Puzicha, “Shape Matching and Object Recognition Using Shape Contexts”, IEEE Trans. on PAMI, 24(4), pp. 509-522, 2002 for 3D shape retrieval and matching, which is defined at a reference point capturing the distribution of the remaining points relative to it. The spin image described in the above document (2) is a data level shape descriptor that is represented as a 2D histogram. These two approaches of the documents (1) and (2) are based on the statistics of local point-sampled geometry, which are appropriate for a variety of shape representations, such as meshes, polygon soups, and oriented point clouds.
Shape distribution described in the above document (3) is a representative global shape descriptor, wherein the signature of an object is represented as a shape distribution sampled from a shape function measuring global geometric properties of an object. There are challenges for this approach on how to select discriminating shape functions and how to develop efficient methods for sampling them. In J. W. H. Tangelder, R. C. Veltkamp, “A Survey of Content Based 3D Shape Retrieval Methods”, Shape Modeling International, pp. 145-156, 2004, a variety of global/local shape descriptors are reviewed for the task of 3D model retrieval.
However, most of the current algorithms for calculating 3D shape descriptors are designed for watertight 3D models, i.e. 3D models with smooth surface and dense vertex distribution. The examples of non-watertight 3D models are shown in FIG. 1. These algorithms are not suitable for non-watertight 3D models, those 3D models with sharp features and sparse vertex distribution, such as architectural and mechanical CAD models. And some applications, such as real-time 3D model searching, need a fast algorithm for calculating 3D shape descriptors.
Therefore, there is a need for a method and apparatus for generating shape descriptor of 3D model, which is efficient for non-watertight 3D models.